Can you fail to find a land?
My opponent plays emrakul, the promised end no controls my next turn. He plays and cracks an arid mesa and says failed to find. He has to play a land from arid mesa as long as there are those lands in the deck right? Arid mesa says to put it on the field
Since Arid Mesa's ability has a player search a library for a card with a given quality (here, "a Mountain or Plains card"), that player "isn't required to find [that card] even if [it's] present in" the library (C.R. 701.19b, 400.2). This is true even if the player who is doing the searching is controlled by another player, in which case the latter player (here, your opponent) can choose whether to find the card called for (C.R. 716.5).
EDIT (Jul. 18, 2020): Some rules were renumbered in the meantime. Add another rule citation.
My opponent plays emrakul promised end no controls my next turn. He plays and cracks an arid mess and says failed to find. He has to play a land from arid mesa as long as there are those lands in the deck right? Arid mesa says to put it on the field
Longer Answer: If a card instructs you to find a card of a specific type, you can fail to find that card:
701.15b If a player is searching a hidden zone for cards with a stated quality, such as a card with a certain card type or color, that player isn’t required to find some or all of those cards even if they’re present in that zone
Why? The card says to search and put on the field. Just like playing a spell that requires you to say, draw a card and deal damage to target creature. If there are no creatures on the field the spell can't be cast.
Why? The card says to search and put on the field. Just like playing a spell that requires you to say, draw a card and deal damage to target creature. If there are no creatures on the field the spell can't be cast.
Arid Mesa's ability doesn't target anything (not even a Mountain or Plains card), since it doesn't identify a target with the word "target", or use a keyword that does so (C.R. 114.1c), so it can be activated regardless of whether its controller has a "Mountain or Plains card" in their library (review C.R. 602.2, 601.2c). See also C.R. 114.10 and 114.10a. This is unlike, say, Peak Eruption, which does have a target, namely a Mountain (C.R. 114.1a).
My opponent plays emrakul, the promised end no controls my next turn. He plays and cracks an arid mesa and says failed to find. He has to play a land from arid mesa as long as there are those lands in the deck right? Arid mesa says to put it on the field
They hate us cause they ain't us.
EDIT (Jul. 18, 2020): Some rules were renumbered in the meantime. Add another rule citation.
Short answer: Yes
Longer Answer: If a card instructs you to find a card of a specific type, you can fail to find that card:
They hate us cause they ain't us.
They hate us cause they ain't us.